Time Crystal in a Single-mode Nonlinear Cavity

TL;DR

This paper demonstrates the realization of a time crystal in a single-mode nonlinear cavity, revealing unique dynamical behaviors and phase transitions associated with non-equilibrium symmetry breaking.

Contribution

It introduces a novel mechanism for time crystal formation via self-oscillation stabilized by nonlinear damping in a single-mode cavity.

Findings

Observation of sharp dissipative gap closing and pure imaginary eigenvalues in the Liouvillian spectrum.

Identification of a dissipative phase transition at the Hopf bifurcation.

Detection of metastable quantum oscillations and rapid dissipative evolution.

Abstract

Time crystal is a class of non-equilibrium phases with broken time-translational symmetry. Here we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear gain and is stabilized by a nonlinear damping. We show in the time crystal phase there are sharp dissipative gap closing and pure imaginary eigenvalues of the Liouvillian spectrum in the thermodynamic limit. Dynamically, we observe a metastable regime with the emergence of quantum oscillation, followed by a dissipative evolution with a time scale much smaller than the oscillating period. Moreover, we show there is a dissipative phase transition at the Hopf bifurcation of the model, which can be characterized by the photon number fluctuation in the steady state. These results pave a new promising way for further experiments and deepen our understanding of time crystals.